Find the equation of the line that contains the point 8 10

Find the equation of the line that contains the point ( 8 ,10 ) and is perpendicular to the line 4 x + 4 y = 4. Write the equation in the form y=mx+b and identify m and b.

m = ______

b =_______

Solution

Given line equation

4x + 4y = 4

To find the slope of the given line we need to get the line into slope-intercept form (y = mx + b), which means we need to solve for y:

4x + 4y = 4

4y = 4 - 4x

y = 1 - x

y = -x + 1

The slope of the line 4x + 4y = 4 is m = –1.

Therefore,

The slope of the line perpendicular to this line would have to be m = 1

Because -1 x 1 = -1

Given point is ( 8 , 10 )

Substitute m = 1 and (8,10) in y = mx + b

10 = 1.8 + b

b = 10 - 8

b = 2

y intercept b = 2

Hence,

m = 1 , b = 2